The Fab Conformations in the Solution Structure of Human Immunoglobulin G4 (IgG4) Restrict Access to Its Fc Region

Background: The human IgG4 antibody subclass does not activate complement and forms half-antibodies. Results: Ultracentrifugation and x-ray/neutron scattering together with atomistic modeling revealed asymmetric concentration-dependent IgG4 solution structures. Conclusion: The complement and receptor Fc binding sites are hindered by the Fab regions, explaining loss of activity. Significance: These solution structures clarify IgG4 function and its therapeutic applications.

Human IgG4 antibody shows therapeutically useful properties compared with the IgG1, IgG2, and IgG3 subclasses. Thus IgG4 does not activate complement and shows conformational variability. These properties are attributable to its hinge region, which is the shortest of the four IgG subclasses. Using high throughput scattering methods, we studied the solution structure of wild-type IgG4(Ser 222 ) and a hinge mutant IgG4(Pro 222 ) in different buffers and temperatures where the proline substitution suppresses the formation of half-antibody. Analytical ultracentrifugation showed that both IgG4 forms were principally monomeric with sedimentation coefficients s 20,w 0 of 6.6 -6.8 S. A monomer-dimer equilibrium was observed in heavy water buffer at low temperature. Scattering showed that the x-ray radius of gyration R g was unchanged with concentration in 50 -250 mM NaCl buffers, whereas the neutron R g values showed a concentration-dependent increase as the temperature decreased in heavy water buffers. The distance distribution curves (P(r)) revealed two peaks, M1 and M2, that shifted below 2 mg/ml to indicate concentration-dependent IgG4 structures in addition to IgG4 dimer formation at high concentration in heavy water. Constrained x-ray and neutron scattering modeling revealed asymmetric solution structures for IgG4(Ser 222 ) with extended hinge structures. The IgG4(Pro 222 ) structure was similar. Both IgG4 structures showed that their Fab regions were positioned close enough to the Fc region to restrict C1q binding. Our new molecular models for IgG4 explain its inability to activate complement and clarify aspects of its stability and function for therapeutic applications.
IgG4 is the only human IgG antibody subclass that does not activate complement (1) and is able to undergo Fab-arm exchange (2) and associate with other IgG molecules via its Fc region (3). Interest in IgG4 arises from its distinct properties compared with the other human IgG subclasses IgG1, IgG2, and IgG3 (4) and its desirability as a pharmaceutical (5). Although the specific function of each IgG subclass remains to be defined, different antigens (e.g. protein, polysaccharide, and allergen) activate varied responses from the four IgG subclasses. IgG4 plasma levels rise after prolonged antigen exposure, leading to anti-inflammatory effects (6). Fab-arm exchange causes IgG4 to behave as if it were monovalent (7), in turn preventing the cross-linking of antibody-antigen complexes and explaining the anti-inflammatory effects of IgG4. IgG4 is popular as a therapeutic as it does not activate complement. However, IgG4 drug products can perform Fab-arm exchange with endogenous IgG4, limiting their efficacy (8). IgG4 can bind to each of the Fc receptor subclasses; however, it does so weakly in comparison with other subclasses (9).
IgG4 Fab-arm exchange is mediated through the Fc region (hinge, C H 2, and C H 3 domains) (10) in which the separation of the two heavy chains to form half-antibodies (half-mers) is attributed to Ser 222 in its core hinge region (supplemental Fig.  S1). Cys 220 and Cys 223 in the core hinge form disulfide bridges between the heavy chains. Mutation of Ser 222 to Pro 222 by genetic engineering gives an IgG1-like core hinge and eliminates half-mer formation (11). Conformational modeling on the two core hinge peptides predicted that the wild-type IgG4(Ser 222 ) hinge is more flexible than the mutant IgG4(Pro 222 ) hinge, perhaps explaining the formation of stable intrachain disulfide bonds in the mutant (12). The equilibrium between these disulfide bridges leads to heterogeneous IgG4 populations, each with two different heavy chains (13). The kinetic rates of half-mer formation in vitro are very low, and Fab-arm exchange does not readily occur. This slow exchange is attributed to strong non-covalent contacts between the C H 3 domains. In fact Fab-arm switching is observed predominantly in vivo.
Fab-arm exchange has been clarified by mutagenesis studies that showed Arg 409 to be crucial for stabilizing the C H 3-C H 3 interaction (Arg 403 in supplemental Fig. S2G) (14 -16). Fabarm switching might be facilitated by protein-disulfide isomerase or binding to the Fc receptor FcRn 2 (4). It has now been shown that Fab-arm exchange requires a combination of factors, predominantly the C H 3 domains and the hinge region, and the presence of a reducing environment; adjuvants are not necessary. IgG1 undergoes Fab-arm switching after replacement of the IgG1 C H 3 domain by the IgG4 C H 3 domain, showing that the IgG4 C H 3 domain is crucial for exchange (17). Interestingly, the Fab regions stabilize the intact IgG4 structure (18). The ability of IgG4 to self-associate is also of interest. IgG4-Fc can interact with IgG1-Fc when IgG1 is coupled to a solid support; the coupling of IgG1 is thought to induce a conformational change, allowing accessibility of its IgG1-Fc for IgG4 binding (3).
An understanding of IgG4 would be facilitated by its atomistic solution structure. Atomistic antibody structures are determined using our joint strategy of x-ray and neutron scattering coupled with analytical ultracentrifugation and constrained modeling based on crystal structures (19 -21). Joint x-ray and neutron scattering allows the study of a broad range of different solution conditions, and this is facilitated by the ability to perform x-ray measurements in seconds rather than minutes. Previously IgG4(Ser 222 ) had been studied by ultracentrifugation and x-ray scattering to show that IgG4 undergoes a concentration-dependent Fab-arm rearrangement (20). This concentration dependence is explored here using more detailed solution structural data for both IgG4(Ser 222 ) and IgG4(Pro 222 ). We show that IgG4(Ser 222 ) and IgG4(Pro 222 ) are principally monomeric, but IgG4(Ser 222 ) shows self-associative behavior in heavy water. Both forms display concentration-dependent structural changes corresponding to Fab-arm rearrangements at low concentrations. Both the IgG4(Ser 222 ) and IgG4(Pro 222 ) solution structures display extended asymmetric arrangements of the Fab regions relative to the Fc region. Our three independently determined IgG4 solution structures showed that the Fab regions were close enough to the Fc region to hinder the C1q and FcR binding sites at the top of the Fc region in IgG4. The implications of this result for the reduced immune reactivity of IgG4 are discussed.

EXPERIMENTAL PROCEDURES
Purification and Composition of IgG4-A wild-type humanmouse chimera, IgG4 B72.3 with Ser 222 , was generously supplied by Dr. Jim Davies (Lonza Biologics) (supplemental Figs. S1 and S2). Other studies named Ser 222 as Ser 228 (22), Ser 229 (12), and Ser 241 (23). A mutant IgG4 with Pro 222 was generously supplied by Dr. Bryan Smith (UCB) (24). Both IgG4(Ser 222 ) and IgG4(Pro 222 ) were further purified by gel filtration to remove nonspecific aggregates using a Superose 6 10/300 column (GE Healthcare), concentrated using an Amicon Ultra spin concentrator (50-kDa-molecular mass cutoff), and dialyzed at 4°C against the measurement buffer (see below). The sequence identity between both IgG4 molecules was 100% for the C H 1, C H 2, and C H 3 domains (except for the S222P substitution). Different identities were found for the V H (67.5%), V L (59.3%), and C L (96.2%) domains, giving an overall identity between the two IgG4 sequences of 86.7% (supplemental Fig. S2). The N-linked oligosaccharides at Asn 291 on the C H 2 domains (supplemental Fig. S2) were assumed to be a complex-type biantennary oligosaccharide structure with a Man 3 -GlcNAc 2 core and two NeuNAc-Gal-GlcNAc antennae (25,26). The IgG4(Ser 222 ) molecular mass was calculated to be 147.0 kDa, its unhydrated volume was 188.7 nm 3 , its hydrated volume was 248.7 nm 3 (based on a hydration of 0.3 g of water/g of glycoprotein and an electrostricted volume of 0.0245 nm 3 per bound water molecule), its partial specific volume v was 0.728 ml/g, and its absorption coefficient was 14.5 (1%, 1-cm pathlength, 280 nm). For IgG4(Pro 222 ), the molecular mass was 149.5 kDa, v was 0.728 ml/g, and the absorption coefficient was 14.1 (27).
Sedimentation Velocity Data for IgG4-Analytical ultracentrifugation data for both IgG4 forms were obtained on two Beckman XL-I instruments equipped with AnTi50 rotors. Sedimentation velocity data were acquired for IgG4(Ser 222 ) samples in PBS-50, PBS-137, and PBS-250 at 20°C; in PBS-137 at 6, 20, and 30°C; and in PBS-137 with 100% 2 H 2 O. Data were collected at rotor speeds of 40,000 and 50,000 rpm in two-sector cells with column heights of 12 mm. Sedimentation velocity data were acquired for IgG4(Pro 222 ) in PBS-137 at 20°C only. Data were collected at rotor speeds of 30,000, 40,000, 50,000, and 60,000 rpm. Sedimentation analysis was performed using direct boundary Lamm fits of up to 700 scans using SEDFIT (version 12.1) (29,30). SEDFIT resulted in size distribution analyses c(s) that assume all species to have the same frictional ratio f/f 0 . The final SEDFIT analyses used a fixed resolution of 200 and optimized the c(s) fit by floating f/f 0 and the baseline until the overall root mean square deviation and visual appearance of the fits were satisfactory. The percentage of oligomers in the total loading concentration was derived using the c(s) integration function.
X-ray and Neutron Scattering Data for IgG4-X-ray scattering data were obtained during a single beam session in 16-bunch mode on Instrument ID02 at the European Synchrotron Radiation Facility, Grenoble, France, operating with a ring energy of 6.0 GeV (31). Data were acquired using a fiber optically coupled high sensitivity and dynamic range charge-coupled device detector (FreLoN) with a resolution of 512 ϫ 512 pixels. A sample-to-detector distance of 3.0 m was used. IgG4(Ser 222 ) in PBS-50, PBS-137, and PBS-250 was studied at 20°C at eight concentrations between 0.48 and 6.91 mg/ml (3.3-47 M) in which 100-l samples were measured in a polycarboxylate capillary (2-mm diameter) that avoids protein deposits during beam exposures. The sample was moved continuously during beam exposure to eliminate radiation damage. Sets of 10 time frames, each of duration 0.1 or 0.2 s/frame, were acquired in quadruplicate as a control of reproducibility. Online checks during data acquisition confirmed the absence of radiation damage after which the 10 frames were averaged. In the same beam session, IgG4(Pro 222 ) in PBS-137 at 20°C was studied at concentrations between 0.5 and 2.0 mg/ml (3.3-13.4 M).
Neutron scattering data were obtained on Instrument SANS2D at the ISIS pulsed neutron source at the Rutherford Appleton Laboratory, Didcot, UK (32). A pulsed neutron beam was derived from proton currents of ϳ40 A. SANS2D scattering and transmission data were recorded with a collimation of 4 m, a sample-to-detector distance of 4 m, a beam diameter of 12 mm, and a wavelength range of 0.175-1.65 nm that was determined by time of flight. IgG4(Ser 222 ) samples were measured in 2-mm-path length circular banjo cells in a thermostated rack at 20°C as well as at 6 and 37°C. Data acquisitions lasted ϳ1-2 h for four samples at concentrations between 2.0 (14 M) and 8.0 mg/ml (55 M) in PBS-137 prepared in 100% heavy water.
In a given solute-solvent contrast, the radius of gyration R g is a measure of structural elongation if the internal inhomogeneity of scattering densities within the protein has no effect. Guinier analyses at low Q (where Q ϭ 4 sin /; 2 is the scattering angle, and is the wavelength) gives the R g and the forward scattering at zero angle I(0) (33).
This expression is valid in a Q⅐R g range up to 1.5. If the structure is elongated, the mean radius of gyration of crosssectional structure R XS and the mean cross-sectional inten- For immunoglobulins, the cross-sectional plot exhibits two regions, a steeper innermost region and a flatter outermost region (34), identified by R XS-1 and R XS-2 , respectively. The R g and R XS analyses were performed using an interactive PERL script program SCTPL7 3 on Silicon Graphics OCTANE Workstations. Indirect transformation of the scattering data I(Q) in reciprocal space into real space to give the distance distribution function P(r) was carried out using the program GNOM (35).  (36,37) as described previously (20). Four sets of 5000 randomized IgG4 models were created using different hinge lengths and compositions. Two sets of asymmetric models were based on the IgG1 crystal structure. For these, a 9-residue hinge peptide, 212 VESKYGPPC 220 , was constrained to be of a minimum length between 2.2 and 3.1 nm or 3.1 and 3.15 nm where the latter is almost fully extended in length. As Cys 220 is located asymmetrically relative to the Fc structure, all these models were conformationally asymmetric. Because this asymmetry may be a crystallographic artifact, two sets of symmetric models were created. For these, a 21-residue hinge peptide, 212 VESKYGPPCPSCPAPEFLGGP 232 , that encompassed the whole hinge was constrained to be of a minimum length between 5.0 and 7.0 nm or between 7.0 and 7.35 nm where the latter is almost fully extended in length. Because Pro 232 is located symmetrically in relation to the Fc structure, the resulting IgG4 models contained Fab regions in both symmetric and asymmetric orientations. The outermost hinge residues were anchor points used to superimpose each hinge conformation onto the Fab and Fc regions to create the full-length IgG4 model. For each of the four sets of 5000 IgG4 models, two different hinge conformations were randomly selected to join the two Fab and Fc regions to form IgG4.
The scattering curve was calculated from each IgG4 model using sphere models. A cube side of 0.557 nm and a cutoff of four non-hydrogen atoms was used to convert the atomic coordinates into 1142 spheres that corresponded to the unhydrated structure seen by neutron scattering. Because hydration shells are visible by x-rays, a hydration shell corresponding to 0.3 g of water/g of protein was created using HYDRO (38), giving an optimal total of 1468 spheres. The x-ray scattering curve I(Q) was calculated using the Debye equation adapted to spheres (39). Details are given elsewhere (26,40). Steric overlap between the Fab and Fc regions was assessed using the number of spheres n in each model where models showing less than 95% of the required total of 1468 spheres (x-ray) or 1142 spheres (neutrons) were discarded. Of the 20,000 hydrated models, 82% showed no steric overlap. The x-ray R g , R XS-1 , and R XS-2 values were calculated from the modeled curves in the same Q ranges used for the experimental Guinier fits. Models that passed R g and R XS filters of Ϯ5% of the experimental value were then ranked using a goodness-of-fit R-factor (defined by analogy with protein crystallography) in the Q range extending to 1.6 nm Ϫ1 . For the neutron modeling, 84% of the 20,000 unhydrated sphere models showed no steric overlap. The neutron models were assessed as for the x-ray scattering models above with corrections for wavelength spread and beam divergence, but no correction was required for a flat background caused from incoherent scattering because of the extrapolation to zero concentration.
Sedimentation coefficients (s 20,w 0 ) were calculated directly from the hydrated Debye sphere models using the program HYDRO (41). They were also calculated from the atomic coordinates in the HYDROPRO shell modeling program using the default value of 0.31 nm for the atomic element radius for all atoms to represent the hydration shell (42). Previous applications of these calculations to antibodies are reviewed elsewhere (43).
The outcome of the fit searches was evaluated by calculating the distances between the centers of mass of the Fab-Fc and Fab-Fab pairs (d1, d2, and d3; excluding hydrogen atoms) using a Python script. The three angles between the Fab and Fc regions were also calculated; these were defined in a Python script as the angle of intersection from the dot product between two vectors. Each vector was defined as the long axis through each Fab or Fc region, each defined as the line passing through the centers of gravity between each cluster of four cysteine ␣-carbon atoms at the two ends of the Fab and Fc regions. One cluster at each end of each Fab or Fc region corresponded to the conserved disulfide bridge in each immunoglobulin fold domain. Artwork was prepared using PyMOL (Schrödinger, LLC). The Fc regions in the 10 best fit IgG4 models were superimposed using the align function within PyMOL. To dock the crystal structures for the Fc region and the C1q head (19), the web server algorithm PatchDock (version beta 1.3) was used to include specified residues as potential binding sites, and then the output was refined using FireDock from the same web site (44).
Protein Data Bank Accession Numbers-The three sets of 10 best fit models are currently available as supplemental material.

RESULTS
Purification of Human IgG4-Wild-type IgG4(Ser 222 ) and its mutant IgG4(Pro 222 ) were subjected to gel filtration to ensure monodispersity immediately prior to the ultracentrifugation and scattering experiments. Both molecules eluted as a symmetric main peak at 16 ml (supplemental Fig. S3) and showed a single band between 200 and 116 kDa in non-reducing SDS-PAGE that corresponds to the expected masses of 147.0 and 149.5 kDa for intact IgG4(Ser 222 ) and IgG4(Pro 222 ), respectively. Under reducing conditions, the heavy chains for both IgG4 molecules were observed at an apparent molecular mass of 55 kDa, and their light chains were between 31 and 21.5 kDa, both as expected (supplemental Fig. S3).
Analytical Ultracentrifugation of Human IgG4-Sedimentation velocity experiments examined the size and shape of IgG4(Ser 222 ) between 0.5 and 8 mg/ml and IgG4(Pro 222 ) between 0.5 and 2.5 mg/ml. The SEDFIT analyses in different NaCl buffers in H 2 O and at different temperatures in 2 H 2 O buffers involved fits of as many as 700 scans, and the good agreement between the experimental boundary scans and fitted lines is clear (Fig. 1, A-C). A major monomer peak was observed at s 20,w 0 values of 6.8 S for IgG4(Ser 222 ) and 6.6 S for IgG4(Pro 222 ). These s 20,w 0 values are consistent with the range of values (6.2-6.9 S) reported previously for human IgG4 (20,(45)(46)(47)(48). Accordingly both IgG4(Ser 222 ) and IgG4(Pro 222 ) were predominantly monomeric in solution and were accompanied by a minor dimer peak.
From the c(s) analyses, the molecular masses of the monomer peak for IgG4(Ser 222 ) were reported as 144 (PBS-50), 145 (PBS-137), and 141 kDa (PBS-250) in light water and 171 (PBS-137 at 6°C), 149 (PBS-137 at 20°C), and 145 kDa (PBS-137 at 30°C) in heavy water. These agree well with the composition-calculated mass of 147 kDa with the exception of PBS-137 in heavy water at 6°C. However, for PBS-137 in heavy water at 6°C, a reaction boundary was observed from the concentration dependence of its monomer peak (Fig. 1B). The molecular mass of the IgG4(Pro 222 ) monomer peak was measured as 143 kDa (PBS-137) in agreement with the composition-calculated mass of 150 kDa.
The apparent sedimentation rates of the IgG4 monomer depended on the buffer composition and temperature ( Fig. 1, A-C). The monomer s 20,w value decreased slightly with rotor speed. For IgG4(Ser 222 ), the monomer s 20,w 0 value was 6.76 S for 40,000 rpm, decreasing to 6.68 S for 50,000 rpm for PBS-137 at 20°C. For IgG4(Pro 222 ), the monomer s 20,w 0 value was 6.64 S for 30,000 rpm, decreasing to 6.59 S for 40,000 rpm, 6.56 S for 50,000 rpm, and 6.53 S for 60,000 rpm. All the IgG4 data reported in this study are for 40,000 rpm. Extrapolation of the s 20,w values to zero concentration gave monomer s 20,w 0 values of 6.71, 6.76, and 6.64 S for the PBS-50, PBS-137, and PBS-250 buffers, respectively, in light water ( Fig. 2A). In PBS-137 in heavy water, the monomer sedimented at apparent rates of 2.75, 4.07, and 5.07 S at 6, 20, and 30°C, respectively (Fig. 1B). When corrected for the buffer density and viscosity of heavy water, s 20,w 0 values of 6.49, 7.22, and 7.35 S, respectively, were obtained. Given that the partial specific volume v for proteins is affected by the hydration shell (27,40) and that the hydration shell for heavy water has a higher mass than that for light water, the v values will be reduced in 100% 2 H 2 O. Additionally, the hydration shell is affected by temperature as shown by the large difference between the s 20,w 0 values at 6 and 30°C. Thus v values of 0.734, 0.716, and 0.713 ml/g were used for 6, 20, and 30°C, respectively, in place of 0.728 ml/g, and these gave final monomer s 20,w 0 values of 6.76 S for each temperature, which are the same as that for PBS-137 in light water. For IgG4(Pro 222 ), the s 20,w 0 value was 6.59 S for PBS-137 at 20°C, which is not significantly different from that for IgG4(Ser 222 ).
The c(s) analyses for IgG4(Ser 222 ) revealed a minor dimer peak at s 20 X-ray and Neutron Scattering of Human IgG4-The solution structure of IgG4 was jointly analyzed by both x-ray and neutron scattering for reproducibility. X-rays in light water buffers monitor the hydration shell as well as the protein structure, whereas neutrons in heavy water buffers monitor the unhydrated structure (see below). X-rays were most effective for looking at IgG4 at 20°C in three different NaCl concentrations. X-ray data collection of IgG4(Ser 222 ) was carried out between 0.48 and 6.91 mg/ml using time frame analyses to ensure the absence of radiation damage effects. Guinier analyses resulted in high quality linear plots in three distinct regions of the I(Q) curves, as expected for antibodies, from which the R g , R XS-1 , and R XS-2 values were obtained within satisfactory Q⅐R g and Q⅐R XS limits (supplemental Fig. S4A and Table 1). The x-ray R g values for IgG4(Ser 222 ) in PBS-50, PBS-137, and PBS-250 showed no concentration dependence with mean values of 4.90, 4.92, and 4.96 nm, respectively (Fig. 3A). The I(0)/c values for IgG4, which were similar at 0.0192, 0.0181, and 0.0179, respectively, also showed no concentration dependence (Fig. 3A). Each of the R XS-1 and R XS-2 values were unchanged among PBS-50, PBS-137, and PBS-250 with mean R XS-1 values of 2.53, 2.56, and 2.51 nm, respectively, and mean R XS-2 values of 1.40, 1.37, and 1.33 nm, respectively. These values agree with the R g , R XS-1 , and R XS-2 values of 4.99, 2.56, and 1.40 nm, respectively, for this same human IgG4(Ser 222 ) molecule in PBS-137 (20). For comparison with IgG4(Ser 222 ), IgG4(Pro 222 ) was studied between 0.5 and 2.0 mg/ml in PBS-137 (supplemental Fig. S4C). The x-ray R g values showed no concentration dependence with a mean value of 4.90 nm (Fig. 3C). Similarly, the I(0)/c values for IgG4(Pro 222 ) were 0.0191, showing no concentration dependence and in agreement with those for IgG4(Ser 222 ) (Fig. 3C). The mean R XS-1 and R XS-2 values were unchanged at 2.60 and 1.37 nm, respectively (Fig. 3C).
Neutron scattering studied the unhydrated protein structure in which the hydration shell is almost invisible in heavy water (40). Neutrons were most useful for temperature studies in PBS-137 because temperature-dependent conditions were less accessible by x-ray scattering. IgG4(Ser 222 ) in 100% 2 H 2 O buffer was analyzed between 2.0 and 8.0 mg/ml. The Guinier analyses revealed high quality linear fits for the same three parameters, R g , R XS-1 , and R XS-2 , as described above for x-rays (supplemental Fig. S4B). The neutron R g values increased with increasing concentration from 5.16 to 5.82 nm at 6°C, from 4.87 to 5.36 nm at 20°C, and from 4.62 to 4.85 nm at 37°C (Fig.  3B). These R g changes were comparatively large, indicating that heavy water promoted IgG4 dimer formation. Because the neutron Guinier fits go to smaller Q values than the x-ray Guinier fits, the neutron fits were more sensitive to dimer formation than the x-ray fits. Extrapolations to zero concentration resulted in R g values of 4.99 (6°C), 4.77 (20°C), and 4.67 nm (37°C). The corresponding I(0)/c values also increased (Fig.  3B). The neutron R XS-1 values decreased slightly with concentration from 2.50 to 2.28 nm at 6°C, from 2.43 to 2.30 nm at 20°C, and from 2.50 to 2.33 nm at 37°C (Fig. 3B). The R XS-2 values showed no concentration dependence with mean values of 1.23, 1.23, and 1.17 nm at 6, 20, and 37°C, respectively (Fig.  3B). The neutron R g , R XS-1 , and R XS-2 values were slightly   smaller than the x-ray values, such as that of 4.92 nm for the R g value in PBS-137, and this reduction is attributed to the near invisibility of the surface hydration shell in heavy water (40) as well as the high negative solute-solvent contrast difference.
The distance distribution function P(r) provides structural information on IgG4 in real space. The x-ray P(r) analyses gave R g and I(0)/c values for IgG4(Ser 222 ) that were similar to those from the x-ray Guinier analyses, showing that the two analyses were self-consistent (Fig. 3A, filled and open symbols). The maximum length L of IgG4 was determined from the value of r when the P(r) curve intersects zero to be 16 nm for PBS-50, PBS-137, and PBS-250 (Fig. 4A). The maxima in the P(r) curves correspond to the most frequently occurring interatomic distances within the structure. For IgG4(Ser 222 ), two peaks, M1 and M2, were identified in many P(r) curves except for that of the 0.5 mg/ml P(r) curve where only M1 was identified. The M1 peak corresponds mostly to distances within each Fab and Fc region, whereas the M2 peak corresponds mostly to distances between pairs of Fab and Fc regions. No buffer dependence in the positions of peaks M1 and M2 was observed. However, the positions of the M2 peaks depended on the IgG4 concentration below 2 mg/ml (Fig. 5A). The more extensive data sets of this study confirmed this dependence seen previously with more limited data (20). The concentration dependence was attributed to a rearrangement of the Fab regions in IgG4(Ser 222 ) in which a 1-2-nm change in the average separation between the Fab-Fc pairs was deduced (20). At concentrations above 2 mg/ml, our new data show that this effect is absent with M1 and M2 being at ϳ4 and 7 nm, respectively (Fig. 5A). The IgG4(Pro 222 ) mutant also showed two M1 and M2 peaks with a similar pronounced shift in the M2 peak (but an unchanged M1 peak) with change in concentration, and the L value was unchanged at 15 nm (Figs. 4C and 5C).
The neutron P(r) analyses reflected IgG4 dimer formation in heavy water. The R g and I(0)/c values for IgG4(Ser 222 ) at 6, 20, and 37°C increased with increasing concentration (Fig. 3B). This was attributed to dimer formation. This result is consistent with the sedimentation velocity experiments where a reaction boundary between monomer and dimer was observed in heavy water at 6 and 20°C (Fig. 1B) but not in light water. The neutron L values were between 17 and 21 nm at 6°C, 16 and 19 nm at 20°C, and 15 and 16 nm at 37°C (Fig. 4B). Thus the greater proportion of dimer at lower temperatures resulted in increased dimensions. Because low amounts of dimer are present, the maximum length of the dimer is probably greater than 21 nm. The two peaks M1 and M2 were again identified at ϳ4 and 7 nm, respectively, in the neutron P(r) curves (Fig. 5B). The positions of M1 and M2 were unchanged between 2 and 8 mg/ml in agreement with the x-ray P(r) data.
Starting Model for the Human IgG4 Scattering Fits-The human IgG4 homology models were created from crystal structures for B72.3 Fab (36) and human IgG1 Fc (37). Details of the sequence alignments, target and template sequence identities, and structure validations are described elsewhere (20). The previous modeling of hinge libraries with 10,000 conformations based on asymmetric IgG4 structures was now extended to include libraries based on symmetric IgG4 structures ("Experimental Procedures"). The full hinge is formally defined by the residues 213 ESKYGPPCPSCPAPEFLGGP 232 (22) in which the Fab region ends at Val 212 and the Fc region starts at Ser 233 a The optimum number n of hydrated (x-rays) and unhydrated (neutrons) spheres predicted from the sequence was 1468 and 1142, respectively. b The first experimental value is from the Guinier R g analysis (Fig. 4), and the second is from the GNOM P(r) analysis (Fig. 5). c The first modeled value corresponds to that from HYDRO, and the second is that from HYDROPRO. d n.a., not applicable.
(supplemental Figs. S1 and S2). The IgG4 hinge contains six Pro residues and two Cys 220 and Cys 223 disulfide bridges. The asymmetric modeling considered only the upper hinge, 212 VESKYGPPC 220 , with Val 212 and Cys 220 acting as tethers. As this hinge is located asymmetrically relative to the Fc region, these 10,000 models do not have 2-fold symmetry. However, the two interchain disulfide bonds are intact. The symmetric modeling considered the upper, middle, and lower hinge, and this resulted in a 21-residue peptide, 212 VESKYGPPCPSCPA-PEFLGGP 232 . Because the two Pro 232 residues were located in the middle of the Fc region, this approach generated both symmetric and asymmetric models. For these 10,000 further models, the Cys 220 and Cys 223 interchain disulfide bonds were not kept intact. mg/ml. These curve fits investigated whether molecular models could rationalize the conformational change seen in IgG4 at below 2 mg/ml for the wild-type and mutant forms of IgG4 (Fig. 5, A and C).  Because IgG4 dimerizes in heavy water, neutron curve fits were based on linear extrapolation of the four experimental curves for IgG4(Ser 222 ) to zero concentration (Fig. 3B). This curve fit examined a single conformation for the IgG4 monomer only. The 10 fit searches were assessed in R-factor versus R g graphs (Fig. 6). In all 10 searches, the occurrence of a single minimum in the R-factor values identified a single family of solution structures for IgG4 starting from a wide range of orientations and translations of the two Fab and Fc regions. The lowest R-factors in the 20,000 curve fits corresponded to modeled R g values close to the experimental R g values as desired.

Conformational Searches for the Human IgG4 Solution
Filters were used to identify the 10 best fit models for each search. (i) A Ϯ5% filter for steric overlap eliminated models in which the Fab and Fc regions sterically overlapped with each other because of inappropriate hinge conformations. To match the composition-calculated volume of IgG4, sphere models needed a minimum number n of 1468 spheres for the hydrated x-ray models and 1142 spheres for the unhydrated neutron models. (ii) A Ϯ5% filter for the modeled R g values (calculated from the same Q ranges used for the experimental analyses) identified the models that agreed best with the experimental x-ray or neutron R g values. (iii) The models that passed the n and R g filters were arranged in order of their lowest R-factors. The resulting 10 best fit models for IgG4 were found as a single cluster at the R-factor minimum in each of the 10 searches (Fig.  6, green).
The two interchain disulfide bonds at Cys 220 and Cys 223 were explicitly conserved in the asymmetric models. For the symmetric models, the pairs of Cys 220 and Cys 223 residues may no longer be proximate. Their ␣-carbon separations were 1.02-3.29 nm for Cys 220 and 1.20 -2.43 nm for Cys 223 in IgG4(Ser 222 ) by x-rays, 0.75-2.18 nm for Cys 220 and 0.98 -1.99 nm for Cys 223 in IgG4(Pro 222 ) by x-rays, and 2.02 nm for Cys 220 and 1.98 nm for Cys 223 for IgG4(Ser 222 ) by neutrons. These ␣-carbon separations were comparable with an expected ␣-carbon separation of 0.4 -0.75 nm between two bridged Cys residues (49).
The best fit modeled curves showed good visual scattering I(Q) and P(r) curve fits in all 10 cases with the experimental curves (Fig. 7). For each case, the R g values for the 10 best fit models were within error of the experimental values ( Table 1). The 10 sets of models in Fig. 8 generally displayed asymmetric arrangements of the two Fab regions compared with the Fc region. Although IgG4(Ser 222 ) showed slightly higher proportions of asymmetric structures compared with the asymmetric and symmetric arrangements seen for IgG4(Pro 222 ), there were no significant differences between the wild-type and mutant structures. Unlike our previous study (20), no gradual continuum between the models at different concentrations was now seen. Surveys of the distances between the centers of the Fab and Fc regions in the best fit IgG4(Ser 222 ) x-ray and neutron models and in the IgG4(Pro 222 ) x-ray models (Figs. 6 and 8) showed similar distributions (supplemental Fig. S5). The x-ray R-factor values for the best fit IgG4 models (Fig. 6, pink) were acceptable at 2.5-4.0% for IgG4(Ser 222 ) and 3.0 -3.6% for IgG4(Pro 222 ) ( Table 1). The neutron R-factor values were acceptable at 2.5-2.7%. These R-factor values are comparable with those from other similar modeling fits (43).
Sedimentation Coefficient Modeling of Human IgG4-The s 20,w 0 values of each of the nine sets of scattering best fit hydrated IgG4 models were calculated for comparison with the experimental values of 6.76 S for IgG4(Ser 222 ) and 6.59 S for IgG4(Pro 222 ) ( Fig. 2A). For the best fit hydrated sphere models, the s 20,w 0 values were 6.76 -6.99 and 6.72-7.02 S for IgG4(Ser 222 ) and IgG4(Pro 222 ), respectively, using HYDRO (Table 1). For the best fit molecular models, the s 20,w 0 values were 6.42-6.94 and 6.23-6.84 S for IgG4(Ser 222 ) and IgG4(Pro 222 ), respectively, using HYDROPRO ( Table 1). Given that the calculations should be accurate to within Ϯ0.21 S (43), both sets of modeled s 20,w 0 values agree well with the experimental values.

DISCUSSION
The large body of x-ray scattering data permitted a detailed appraisal of the solution structure of human IgG4, and this was supported by complementary neutron scattering and ultracentrifugation experiments. The scattering data enabled atomistic conformational analyses of IgG4 that resulted in three independent determinations of an asymmetric IgG4 solution structure. The combination of the resulting three IgG4 solution structures with (i) a recent docking model for the interaction between human Fc and the crystal structure of the C1q globular head (19,50) and (ii) crystal structures for the human Fc-Fc␥R receptor (51,52) has provided new clarity on the lack of reactivity of human IgG4 with its two major effector ligands.
IgG4 has the lowest IgG serum concentration of the four IgG subclasses at an average level of 0.4 mg/ml (in a range of 0.2-1 mg/ml). The data collection of our IgG4 study utilized a concentration range of 0.4 -8.0 mg/ml, which spanned the serum range and above. IgG1 is the most common subclass at 8 mg/ml (in a range of 5-12 mg/ml) followed by 4 mg/ml for IgG2 (in a range of 2-6 mg/ml) and 0.8 mg/ml for IgG3 (in a range of 0.5-0.1 mg/ml) (1). Although distinct immune roles for each of the four IgG subclasses are yet to be elucidated, IgG4 is thought to have anti-inflammatory properties, and the plasma levels of IgG4 rise in response to repeated antigen exposure. IgG4 is unable to activate complement via C1q binding in the complement classical pathway and binds weakly to Fc␥R receptors (9). IgG4 also has the ability to form half-mers comprising a single FIGURE 6. Constrained modeling analysis for IgG4. The 20,000 goodness-of-fit R-factors are compared with the x-ray and neutron R g values for the conformationally randomized IgG4(Ser 222 ) models. The 20,000 asymmetric and symmetric models are shown in yellow. The 10 best fit models with the lowest R-factors are shown in green of which the best fit model is shown in pink. The experimentally observed R g values are shown by vertical solid lines to follow the Guinier R g values (Table 1) with Ϯ5% error ranges shown as dashed lines. A, the hydrated x-ray models are compared with the x-ray curves for IgG4(Ser 222 ) in PBS-137 for each of five concentrations between 0.5 and 6 mg/ml. B, the unhydrated neutron models are compared with the neutron curve for IgG(Ser 222 ) in PBS-137 in 2 H 2 O after linear extrapolation to 0 mg/ml. C, the hydrated x-ray models are compared with the x-ray curves for IgG4(Pro 222 ) in PBS-137 for each of four concentrations between 0.5 and 2 mg/ml. pair of light and heavy chains; thus IgG4 is able to undergo Fab-arm switching and become bispecific.
Solution Structure of Wild-type IgG4(Ser 222 )-For IgG4(Ser 222 ), our x-ray data collection involved measurement of 192 curves (or 1920 curves if time frames are included) within 2 h (Fig. 3). This high data collection rate permitted the study of its solution structure in different buffers as well as the comparison of the wild-type and mutant forms. Because antibodies are considered to possess flexible hinge structures, the use of three NaCl concentrations will test the potential effects of flexibility on the IgG4 structure. In addition, neutrons permitted the study of IgG4 in heavy water buffer at three temperatures (Fig. 3). All six conditions were replicated using ultracentri- fugation (Fig. 1). In contrast, earlier studies reported few scattering and ultracentrifugation runs, which limited the evaluation of potential buffer-dependent IgG4 conformations (45)(46)(47)(48).
Despite an expectation that flexible hinge structures would be revealed by scattering, our wild-type IgG4(Ser 222 ) data collection indicated no observable change in the R g , M1/M2, or s 20,w 0 values in concentrations between 2 and 8 mg/ml in six buffers and temperatures (Figs. 3 and 5). This outcome suggests lack of conformational change in its averaged solution structure. However, below 2 mg/ml, both IgG4(Ser 222 ) and IgG4(Pro 222 ) showed reproducible concentration-dependent changes in the M2 peak that monitors the mean separation between the Fab-Fab and Fab-Fc pairs (Fig. 5). These M2 changes were similar to those reported previously by us for IgG4(Ser 222 ) (20). Thus, in the most dilute conditions, the Fab regions underwent 1-2-nm movements relative to the Fc region to affect M2 but not the R g or s 20,w 0 values. Potential molecular mechanisms for this rearrangement are discussed below.
The scattering modeling fits revealed asymmetric IgG4 molecular structures for the Fab and Fc regions and their connecting hinge in which (i) the IgG4 hinge structures are extended in solution and (ii) the arrangement of the Fab and Fc regions is unaffected by different buffers. IgG4 was modeled starting from the intact IgG1 b12 molecule in which the lower hinge was asymmetrically arranged (37). To avoid bias in our modeling, both asymmetric and symmetric hinge structures were tested ("Experimental Procedures"). All 10 modeling fits showed that its Fab and Fc arrangement was asymmetric. These asymmetric solution structures (Figs. 6 -8) are the consequence of its relatively short hinge sequence and the need to accommodate both Fab regions close to the Fc region. Thus the hinge is too short to permit unrestricted conformations of the Fab regions about the Fc region. The IgG4 upper hinge is 7 residues long. Its middle hinge is 5 residues long and contains two interchain disulfide bonds. In the IgG4 models, the ␣-carbon distances between the Cys 220 -Cys 220 and Cys 223 -Cys 223 pairs turned out to be within acceptable limits. There is evidence that the inter-and intrachain disulfide bonds are in equilibrium (13); therefore the hinge disulfide bonds are not necessarily maintained intact. Even if these bonds become separated, IgG4 remains intact due to contacts between the C H 3 domain pairs as shown by sedimentation velocity (Fig. 1). These asymmetric solution structures resemble crystal structures for intact IgG. Three asymmetric structures include human IgG1 b12 (Protein Data Bank code 1HZH (37)), murine IgG2a 231 (Protein Data Bank code 1IGT (53)), and murine IgG1 61.1.3 (Protein Data Bank code 1IGY (54)). A fourth hinge-deleted human IgG1 Mcg structure, however, showed a symmetric structure (Protein Data Bank code 1MCO (55)). Our results differ from a previous determination of a symmetric structure for wild-type IgG4 based on simple ellipsoid models for the Fab and Fc regions; large differences in that study between the modeled and experimental x-ray curves do not substantiate this symmetric structure (see Fig. 4d of Ref. 45). This is in contrast to our improved curve fits from atomistic modeling based on asymmetric structures (Fig. 7).
After this study was completed, two crystal structures for human IgG4 Fc were published, namely those for a recombinant and a serum-derived Fc fragment (Protein Data Bank codes 4C54 and 4C55 (56). These structures showed conformational variability around Arg 409 and a unique conformation of the FG loop in the C H 2 domain when compared with human IgG1 Fc. These two structural features were linked with the Fab-arm exchange behavior and the reduced binding of FcRs to IgG4, respectively. Our homology-modeled Fc structure in the IgG4(Ser 222 ) best fit models was compared with the IgG4 Fc crystal structures. The root mean square difference in ␣-carbon positions when superimposed was low at 0.0937 and 0.0841 nm (Protein Data Bank codes 4C54 and 4C55, respectively). When the Fc region in the scattering best fit model for IgG4(Ser 222 ) was replaced with the Fc crystal structures, the resulting R-factors of 2.7 (Protein Data Bank code 4C54) and 2.9% (Protein Data Bank code 4C55) were almost unchanged compared with that of 2.8% for the best fit model ( Table 1).
Comparison of Wild-type and Mutant IgG4-Wild-type and mutant IgG4 differ through the S222P substitution in its hinge. This change to Pro abolishes half-mer formation and presumably results from the reduced flexibility of the hinge (11,12). Our experimental data showed that the wild-type and mutant forms had similar experimental R g and R XS values (Table 1). Although IgG4(Pro 222 ) has a slightly shorter overall length at 15 nm compared with 16 nm for IgG4(Ser 222 ), its s 20,w 0 value is slightly smaller at 6.6 S compared with 6.8 S for IgG4(Ser 222 ). Both forms showed decreased s 20,w 0 values when the concentration went below 2 mg/ml. Experimentally both forms were indistinguishable within error.
The best fit structures for IgG4(Ser 222 ) are predominantly asymmetric, especially at the highest concentrations (Fig. 8A). At lower concentrations, both IgG4(Ser 222 ) and IgG4(Pro 222 ) displayed a combination of asymmetric and symmetric best fit structural models. Although the IgG4(Pro 222 ) form is thought to be less flexible (12), the modeling showed little difference between the two forms. The modeling showed that the hinge in both IgG4 forms is mostly extended. This hinge length is measured by the ␣-carbon positions of the flanking residues Val 212 and Pro 232 with a maximum possible length of 7.0 nm. The five IgG4(Ser 222 ) hinge lengths decreased slightly with increasing concentration (Fig. 8A). In fact, each of the three final best fit structures gave similar hinge lengths of 4.99 -5.73 Ϯ 1.08 nm for IgG4(Ser 222 ) and 4.81-5.94 Ϯ 1.08 nm for IgG4(Pro 222 ) in PBS-137 and 5.58 Ϯ 1.10 nm for IgG4(Ser 222 ) in PBS-137 in heavy water.
Restricted Interaction of Human IgG4 with C1q-Our full structural models for IgG4 permit the re-evaluation of why C1q is not able to bind to IgG4. Initially C1q had been represented by a sphere of the same volume as its crystal structure so that C1q binding to its Fc binding site could be studied by classic solvent accessibility calculations (20,57). This simplified approach suggested that the Fab regions in IgG4 obstructed the IgG4 interaction with C1q. Here we performed molecular docking of the Fc and C1q crystal structures to re-evaluate this interaction. This approach had previously shown that the rabbit IgG interaction with C1q was allowed (19,50).
The reactivity of complement C1q with the four human IgG subclasses correlates with hinge length in the order IgG3 Ͼ IgG1 Ͼ IgG2 Ͼ IgG4) (1). Given that human IgG4 with the shortest hinge length does not activate complement, this implies that the hinge length is also important for activation. Human IgG residues implicated in C1q binding include Asp 270 , Lys 322 , Pro 329 , and Pro 331 in the Fc region (58,59). This C1q binding site occurs at the top of the C H 2 domain in the Fc region. The Fab regions in both our IgG4(Ser 222 ) and IgG4(Pro 222 ) models are positioned close to the IgG4 binding site for C1q, potentially hindering C1q binding. Docking studies were performed using a shape complementarity method by the PatchDock server (19). This was based on the 19 C1q and 12 Fc contact residues identified for the IgG1-C1q complex (see Table 2 in Ref. 50). It should be noted that 2 residues were substituted in IgG4 when compared with IgG1 (His 268 with Gln 268 and Pro 331 with Ser 331 , denoted as Gln 262 and Ser 325 , respectively, in supplemental Fig. S2). In contrast to the rabbit IgG-C1q interaction, our docked IgG4-C1q structures (Fig. 9, A and B) show that the C1q head is sterically hindered by the Fab regions from interacting with the top of the Fc region in IgG4. In addition, biochemical studies using domain-switched chimeric antibodies showed that the differential complement activation of the subclasses resided in the COOH-terminal C H 2 domain (60). Mutagenesis studies showed that Ser 331 in IgG4 was critical for the inability of IgG4 to bind C1q and activate complement. Interestingly, the strength of C1q binding to IgG4 was distinct from its ability to activate complement; thus changes in other parts of IgG4 may be necessary for effective complement activation (61). In conclusion, a combination of steric hindrance from the Fab regions in IgG4, the restricted movement of the IgG4 hinges, and the importance of Ser 331 for the Fc-C1q interaction appear to account for the lack of binding of C1q to IgG4. The unique conformation of the FG loop in the C H 2 domains in the crystal structure of IgG4-Fc on which Ser 331 is located is likely to be relevant too (56).
Restricted Interaction of Human IgG4 with Fc␥R-Many distinct Fc␥Rs are present on immune cells, including monocytes, neutrophils, platelets, and lymphocytes (1), with diverse functions within the immune system. In general, Fc␥R binding to IgG activates antibody-dependent cell-mediated cytotoxicity events, although individual Fc␥Rs may have activator or inhibitor effects. Differences between the activities of the four IgG subclasses are attributed to their individual affinity for specific Fc␥Rs, hence stimulating a specific and predictable response to certain pathogens (62). The affinities of the four human IgG   (63).
The IgG Fc residues implicated in Fc␥R binding include Leu 234 -Leu 235 -Gly 236 -Gly 236 -Gly 237 -Pro 238 of the lower hinge region (64). The Fc glycan interactions with Fc␥R are important to stabilize the interaction (65,66). A 1:1 stoichiometry of this interaction has been determined by sedimentation equilibrium (67,68). The ability of IgG to bind two Fc␥R molecules may be sterically hindered due to a conformational change upon binding of the first Fc␥R molecule (69). Crystal structures of the IgG1 Fc-Fc␥RIIIB complex show that Fc␥R binds to the top of the Fc region close to the hinge (51,52). The corresponding IgG4-Fc␥R interaction was revealed by superimposition of our best fit IgG4(Ser 222 ) and IgG4(Pro 222 ) solution structures on these crystal structures. This showed that Fc␥R binding appears to be permitted. Given that the Fab regions in our IgG4 models are close to the top of the Fc region where the Fc␥Rs bind, these Fab regions may offer steric hindrance to binding (Fig. 9, C and D). However, as IgG4 is able to bind most Fc␥Rs (albeit not as strongly as the IgG1 and IgG3 subclasses), a small movement of the Fab region in our IgG4 models may permit binding to take place, and the strength of binding between Fc and Fc␥R may be primarily determined by the residues present in the hinge and C H 2 domains. In this context, IgG4 possesses Phe 234 in comparison with IgG1 and IgG3 in which this is Leu 234 and with IgG2, which has a shorter lower hinge region with Val 234 and Ala 236 substitutions and the deletion of Leu 235 . IgG4 also has a shorter overall hinge length, which may lead to weaker Fc␥R binding (70). The higher affinity of IgG4 for Fc␥RI may be due to an additional extracellular domain in comparison with the two in Fc␥RII and Fc␥RIII or structural differences in this additional domain, leading to its greater affinity (71).
Stability of Human IgG4-Antibody stability is a major concern in the context of the Ͼ$30 billion antibody industry. Stabilities may be compromised during manufacturing, shipping, and storage (72). In the context of bioprocessing, the internal stability of human IgG4 was explored here using different buffers and temperatures by x-ray and neutron scattering. The movement of the M2 peaks below 2 mg/ml confirmed our earlier observations (20). This M2 shift revealed an internal structural rearrangement of the Fab and Fc regions, although here we were not able to model this. In addition, our x-ray and neutron data showed that this rearrangement was stabilized at concentrations higher than 2 mg/ml (Fig. 5). As similar movements of M2 were seen in different NaCl concentrations, this indicated that charge effects within IgG4 or between IgG4 molecules were not responsible for this change. The M2 peak shifts may relate to a diffusion-collision phenomenon (which would be charge-independent) in which more frequent collisions between IgG4 molecules at higher concentrations would lead to a more compact molecular conformation for IgG4. Alternatively the M2 peak shifts may relate to Fab-arm exchange in which the half-mers in IgG4 are more likely to rearrange themselves and dissociate in dilute conditions, leading to conformational instabilities.
To understand better how a diffusion-collision process might lead to conformational change in IgG4, this process can be considered as an equilibrium where collisions between IgG4 molecules at higher concentrations lead to a deformed shape that can relax back to the unperturbed shape in dilute solution. Above 2 mg/ml, the rate of collisions (k coll ) would be greater than the relaxation rate, leading to a deformed IgG4 structure. The upper limit for the relaxation rate is therefore defined by the collision rate constant k coll for 2 mg/ml. The collisional frequency Z can be calculated using the diffusion coefficient from SEDFIT and the radius of IgG4 from Equation 4.

Z ϭ
4N͑D A ϩ D B ͒͑r A ϩ r B ͒ 1000 (Eq. 4) where N is Avogadro's number (6.02214 ϫ 10 Ϫ23 ), D is the diffusion coefficient (4.07 ϫ 10 Ϫ11 m 2 s Ϫ1 ), and r is the radius for two IgG4 monomers A and B. This gives a collision frequency of 6300 M Ϫ1 s Ϫ1 . The k coll value can be calculated from Equation 5.
If the transmission factor p is 1 (i.e. collisions between molecules always lead to a conformational change) and E act is 0, then the equation is simplified to k coll ϭ Z. At 2 mg/ml (14 M), the upper limit for the relaxation rate is obtained by multiplying k coll by the concentration to give 88 s Ϫ1 . Because the calculation assumes that all collisions lead to a shape change, which is unlikely, the true rate of relaxation will be lower than 88 s Ϫ1 . Fab-arm exchange through half-mer formation leads to bispecificity in human IgG4 (7). This process leads to the exchange of therapeutic IgG4 molecules with endogenous IgG4 molecules in vivo (8). Fab-arm exchange was shown to be a dynamic process (17), and the mechanism of Fab-arm exchange is controlled by local redox conditions (18). Human IgG4 also can exchange with isolated IgG4 Fc fragments, indicating that it is the Fc region that is important for Fab-arm exchange (10). Half-mer was observed for both IgG4(Ser 222 ) and IgG4(Pro 222 ) by non-reducing SDS-PAGE as a faint band at ϳ75 kDa (supplemental Fig. S3). However, these bands have been shown to be artifacts formed under the harsh conditions of SDS-PAGE and depend on heating times and the SDS buffers (73). No halfmer peaks were directly observed in this study by gel filtration or analytical ultracentrifugation (Fig. 1). This indicated that Fab-arm exchange via half-mer formation is slow, but the halfmer life time is short. The low population of half-mer would not be visible by our gel filtration or analytical ultracentrifugation experiments. The movement of the M2 peaks in dilute conditions may predispose the IgG4 molecules to exchange halfmers, perhaps following collisions between two different IgG4 molecules.
Another aspect relevant to antibody bioprocessing relates to IgG4 dimer formation and self-association. Extensive dimer formation may lead to nonspecific antibody aggregation. Indeed, rabbit IgG was observed to form as much as 25% dimer in heavy water buffers, possibly arising through Fab-Fab pairings between the two monomers (19). The low amount of IgG4 dimer observed by sedimentation velocity in six different buffers ( Fig. 1) showed that IgG4 does not undergo extensive buffer-dependent dimerization. The dimer peak has an s 20,w 0 value of about 10 S, suggesting that dimers may arise from a compact association of the Fab and Fc regions. However, a concentration-dependent reaction boundary was observed for IgG4(Ser 222 ) in heavy water, especially at reduced temperature (Fig. 1B). This indicated fast on/fast off association rates between monomer and dimer. Neutron scattering confirmed the temperature-dependent self-association in heavy water (Fig. 3B). Greater dimer formation in heavy water is attributed to weaker hydrogen bonding in this solvent, meaning that protein-protein interactions are promoted. In other studies, IgG4 has been shown to associate with the Fc fragments of other IgG classes, probably occurring between their C H 3 domains (10). The self-association of IgG4 molecules through the C H 3 domains may be an intermediate before half-mer swapping. IgG4 can also associate with IgG1 following a conformational change of IgG1 that exposes the IgG1 C H 3 domains (3). We conclude that dimer formation and self-association events may be relevant to the bioprocessing properties of IgG4.